Weijian Zhang

Jiahao Chen, Weijian Zhang

Evolving graphs arise in problems where interrelations between data change over time. We present a breadth first search (BFS) algorithm for evolving graphs that computes the most direct influences between nodes at two different times. Using simple examples, we show that naive unfoldings of adjacency matrices miscount the number of temporal paths. By mapping an evolving graph to an adjacency matrix of an equivalent static graph, we prove that our generalization of the BFS algorithm correctly accounts for paths that traverse both space and time. Finally, we demonstrate how the BFS over evolving graphs can be applied to mine citation networks.

William C. Yau, Weijian Zhang, Hashan Kavinga Weerasooriya et al.

Depth estimation using a single-photon LiDAR is often solved by a matched filter. It is, however, error-prone in the presence of background noise. A commonly used technique to reject background noise is the rank-ordered mean (ROM) filter previously reported by Shin \textit{et al.} (2015). ROM rejects noisy photon arrival timestamps by selecting only a small range of them around the median statistics within its local neighborhood. Despite the promising performance of ROM, its theoretical performance limit is unknown. In this paper, we theoretically characterize the ROM performance by showing that ROM fails when the reflectivity drops below a threshold predetermined by the depth and signal-to-background ratio, and its accuracy undergoes a phase transition at the cutoff. Based on our theory, we propose an improved signal extraction technique by selecting tight timestamp clusters. Experimental results show that the proposed algorithm improves depth estimation performance over ROM by 3 orders of magnitude at the same signal intensities, and achieves high image fidelity at noise levels as high as 17 times that of signal.

Stanley H. Chan, Hashan K. Weerasooriya, Weijian Zhang et al.

Single-photon Light Detection and Ranging (LiDAR) systems are often equipped with an array of detectors for improved spatial resolution and sensing speed. However, given a fixed amount of flux produced by the laser transmitter across the scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease when more pixels are packed in a unit space. This presents a fundamental trade-off between the spatial resolution of the sensor array and the SNR received at each pixel. Theoretical characterization of this fundamental limit is explored. By deriving the photon arrival statistics and introducing a series of new approximation techniques, the Mean Squared Error (MSE) of the maximum-likelihood estimator of the time delay is derived. The theoretical predictions align well with simulations and real data.

Hashan K. Weerasooriya, Prateek Chennuri, Weijian Zhang et al.

Single-Photon Light Detection and Ranging (SP-LiDAR is emerging as a leading technology for long-range, high-precision 3D vision tasks. In SP-LiDAR, timestamps encode two complementary pieces of information: pulse travel time (depth) and the number of photons reflected by the object (reflectivity). Existing SP-LiDAR reconstruction methods typically recover depth and reflectivity separately or sequentially use one modality to estimate the other. Moreover, the conventional 3D histogram construction is effective mainly for slow-moving or stationary scenes. In dynamic scenes, however, it is more efficient and effective to directly process the timestamps. In this paper, we introduce an estimation method to simultaneously recover both depth and reflectivity in fast-moving scenes. We offer two contributions: (1) A theoretical analysis demonstrating the mutual correlation between depth and reflectivity and the conditions under which joint estimation becomes beneficial. (2) A novel reconstruction method, "SPLiDER", which exploits the shared information to enhance signal recovery. On both synthetic and real SP-LiDAR data, our method outperforms existing approaches, achieving superior joint reconstruction quality.

Xiaoyuan Zhu, Kimberly Le Truong, Riccardo Fogliato et al.

As LLMs are deployed in high-stakes settings, users must judge the correctness of individual responses, often relying on model-generated justifications such as reasoning chains or explanations. Yet, no standard measure exists for whether these justifications help users distinguish correct answers from incorrect ones. We formalize this idea as error verifiability and propose $v_{\text{bal}}$, a balanced metric that measures whether justifications enable raters to accurately assess answer correctness, validated against human raters who show high agreement. We find that neither common approaches, such as post-training and model scaling, nor more targeted interventions recommended improve verifiability. We introduce two methods that succeed at improving verifiability: reflect-and-rephrase (RR) for mathematical reasoning and oracle-rephrase (OR) for factual QA, both of which improve verifiability by incorporating domain-appropriate external information. Together, our results establish error verifiability as a distinct dimension of response quality that does not emerge from accuracy improvements alone and requires dedicated, domain-aware methods to address.

Zhiwei Zhang, Ruikai Xu, Weijian Zhang et al.

In this paper, we present the first pinhole-fisheye framework for heterogeneous multi-view depth estimation, PFDepth. Our key insight is to exploit the complementary characteristics of pinhole and fisheye imagery (undistorted vs. distorted, small vs. large FOV, far vs. near field) for joint optimization. PFDepth employs a unified architecture capable of processing arbitrary combinations of pinhole and fisheye cameras with varied intrinsics and extrinsics. Within PFDepth, we first explicitly lift 2D features from each heterogeneous view into a canonical 3D volumetric space. Then, a core module termed Heterogeneous Spatial Fusion is designed to process and fuse distortion-aware volumetric features across overlapping and non-overlapping regions. Additionally, we subtly reformulate the conventional voxel fusion into a novel 3D Gaussian representation, in which learnable latent Gaussian spheres dynamically adapt to local image textures for finer 3D aggregation. Finally, fused volume features are rendered into multi-view depth maps. Through extensive experiments, we demonstrate that PFDepth sets a state-of-the-art performance on KITTI-360 and RealHet datasets over current mainstream depth networks. To the best of our knowledge, this is the first systematic study of heterogeneous pinhole-fisheye depth estimation, offering both technical novelty and valuable empirical insights.

Weijian Zhang, Jonathan Deakin, Nicholas J. Higham et al.

We present Etymo (https://etymo.io), a discovery engine to facilitate artificial intelligence (AI) research and development. It aims to help readers navigate a large number of AI-related papers published every week by using a novel form of search that finds relevant papers and displays related papers in a graphical interface. Etymo constructs and maintains an adaptive similarity-based network of research papers as an all-purpose knowledge graph for ranking, recommendation, and visualisation. The network is constantly evolving and can learn from user feedback to adjust itself.